Annals of West University of Timisoara - Mathematics and Computer Science, 2019
The previous title takes some precautions, which are visible, but still I want to stress them. Fi... more The previous title takes some precautions, which are visible, but still I want to stress them. First, the autobiographical character. The last two decades-to be precise, the last twenty two years-I was totally dedicated to bio-computability, one can even say that I was confiscated by this research area, so fascinating, promising, endless in possibilities of theoretical developments and of applications. The beginning is placed in the spring of 1994, when I read a paper by Tom Head, a wise American who later became a friend and a collaborator of mine, who, already in 1987, proposed a formal language theory model for the recombination operation of DNA under the influence of restriction enzymes and ligase. He has named it the splicing operation. I will shortly describe it later. I remember it exactly-I was in Austria, in Graz, participating in a conference. On the one hand, I became immediately enthusiastic about this idea-after two decades of research in formal language theory, I was subconsciously looking for areas to apply this theory, on the other hand, I was somewhat unsatisfied, because Head's formalization was complex, it remained, to my taste, too close to the biological reality. Right then, in the hotel in Graz, I have imagined a simpler definition, closer to the style I was used, I can call it Salomaa-Marcus style. Four years after that I have worked This is the English version of a lecture delivered on
A series of open problems and research topics are formulated, about numerical and spiking neural ... more A series of open problems and research topics are formulated, about numerical and spiking neural P systems, initially prepared as a working material for a three months research stage of the second and the third co-author in Curtea de Argeş, Romania, in the fall of 2015. Further problems were added during this period, while certain problems were addressed in this time; some details and references are provided for such cases.
As mentioned above, the meeting was organized by the Research Group on Natural Computing from Sev... more As mentioned above, the meeting was organized by the Research Group on Natural Computing from Sevilla University (http://www.gcn.us.es) and all its members were enthusiastically involved in this (not always easy) work.
Spiking neural P systems (SN P systems, for short) are much investigated in the last years in mem... more Spiking neural P systems (SN P systems, for short) are much investigated in the last years in membrane computing, but still many open problems and research topics are open in this area. Here, we first recall two such problems (both related to neural biology) from [15]. One of them asks to build an SN P system able to store a number, and to provide it to a reader without losing it, so that the number is available for a further reading. We build here such a memory module and we discuss its extension to model/implement more general operations, specific to (simple) data bases. Then, we formulate another research issue, concerning pattern recognition in terms of SN P systems. In the context, we define a recent version of SN P systems, enlarged with rules able to request spikes from the environment; based on this version, so-called SN dP systems were recently introduced, extending to neural P systems the idea of a distributed dP automaton. Some details about such devices are also given, as a further invitation to the reader to this area of research.
A series of open problems and research topics are formulated, about numerical and spiking neural ... more A series of open problems and research topics are formulated, about numerical and spiking neural P systems, initially prepared as a working material for a three months research stage of the second and the third co-author in Curtea de Argeş, Romania, in the fall of 2015. Further problems were added during this period, while certain problems were addressed in this time; some details and references are provided for such cases.
In the style of previous meetings in this series, the ninth BWMC was conceived as a period of act... more In the style of previous meetings in this series, the ninth BWMC was conceived as a period of active interaction among the participants, with the emphasis on exchanging ideas and on cooperation. Interesting enough, both the number of presentations and the number of participants have continuously increased in the last years. (The list of the participants is given in the end of this preface.) However, in the style of the of this series of meeting, these presentations were \provocative", mainly proposing new ideas, open problems, research topics, results which need further improvements. The eciency of this type of meetings was again proved to be very high and the present volume proves this assertion. The papers included in this volume, arranged in the alphabetic order of the authors, were collected in the form available at a short time after the brainstorming; several of them are still under elaboration. The idea is that the proceedings are a working instrument, part of the interaction started during the stay of authors in Sevilla, meant to make possible a further cooperation, this time having a written support. A selection of the papers from this volume will be considered for publication in a special issues of
Two research directions on numerical P systems and two on spiking neural P systems which were rec... more Two research directions on numerical P systems and two on spiking neural P systems which were recently explored are shortly discussed. They deal with very natural versions of these classes of P systems which were not investigated before. Besides definitions, one recalls a few of the results obtained about these new classes of P systems and one points out open problems and directions for further research.
As mentioned above, the meeting was organized by the Research Group on Natural Computing from Sev... more As mentioned above, the meeting was organized by the Research Group on Natural Computing from Sevilla University (http://www.gcn.us.es)-and all the members of this group were enthusiastically involved in this (not always easy)
We continue the line of research of deterministic parallel non-cooperative multiset rewriting wit... more We continue the line of research of deterministic parallel non-cooperative multiset rewriting with control. We here generalize control, i.e., rule applicability context conditions, from promoters and inhibitors checking presence or absence of certain object up to some bound, to regular and even stronger predicates, focusing at predicates over multiplicity of one symbol at a time. 3 the meaning of a promoter-set in [3] is different, but the computational power results are equivalent up to the descriptional complexity parameters such as number of promoters/inhibitors and their weights
This note considers three basic research directions in membrane computing-characterizations of th... more This note considers three basic research directions in membrane computing-characterizations of the computing power of Turing machines, computing more than Turing machines, efficiency (solving computationally hard problems in a feasible time)-by basic classes of P systems (cell and tissue multiset rewriting systems, symport/antiport systems, spiking neural P systems, numerical P systems). (Types of) Results reported in the literature are briefly mentioned, several unsolved cases are pointed out, and directions of further research are proposed.
International Journal of Computers Communications & Control, 2015
Three are the points we briefly discuss here: using membrane computing tools for efficient comput... more Three are the points we briefly discuss here: using membrane computing tools for efficient computing/optimization, the possibilities of using “general" membrane computing (P systems using multisets of symbol objects processed by biochemical-like evolution rules) as a framework for modeling economic processes, and the numerical P systems, a class of computing devices explicitly defined with a motivation related to economics. The discussion is rather informal, only pointing out research directions and providing bibliographical information.
Seventh Brainstorming Week on Membrane Computing Vol 2 Miguel Angel Martinez Del Amor 2009 Isbn 9788461328390 Pags 197 206, 2009
A few open problems and research topics collected during the 7th Brainstorming Week on Membrane C... more A few open problems and research topics collected during the 7th Brainstorming Week on Membrane Computing are briefly presented; further details can be found in the papers included in the volume.
In search for "realistic" bio-inspired computing models, we consider asynchronous spiking neural ... more In search for "realistic" bio-inspired computing models, we consider asynchronous spiking neural P systems, in the hope to get a class of computing devices with decidable properties. However, although the non-synchronization is known in general to decrease the computing power, in the case of using extended rules (several spikes can be produced by a rule) we obtain again the equivalence with Turing machines (interpreted as generators of sets of vectors of numbers). The problem remains open for the case of restricted spiking neural P systems, whose rules can only produce one spike. On the other hand, we prove that asynchronous spiking neural P systems, with a specific way of halting, using extended rules and where each neuron is either bounded or unbounded, are equivalent to partially blind counter machines and, therefore, have many decidable properties.
In order to enhance the efficiency of spiking neural P systems, we introduce the features of neur... more In order to enhance the efficiency of spiking neural P systems, we introduce the features of neuron division and neuron budding, which are processes inspired by neural stem cell division. As expected (as it is the case for P systems with active membranes), in this way we get the possibility to solve computationally hard problems in polynomial time. We illustrate this possibility with SAT problem.
The concept of a matter object being annihilated when meeting its corresponding anti-matter objec... more The concept of a matter object being annihilated when meeting its corresponding anti-matter object is investigated in the context of membrane systems, i.e., of (distributed) multiset rewriting systems applying rules in the maximally parallel way. Computational completeness can be obtained with using only non-cooperative rules besides these matter/anti-matter annihilation rules if these annihilation rules have priority over the other rules. Without this priority condition, in addition catalytic rules with one single catalyst are needed to get computational completeness. Even deterministic systems are obtained in the accepting case. Universal P systems with a rather small number of rules-57 for computing systems, 59 for generating and 52 for accepting systemscan be constructed when using non-cooperative rules together with matter/anti-matter annihilation rules having weak priority. Allowing anti-matter objects as input and/or output, we even get a computationally complete computing model for computations on integer numbers. Interpreting sequences of symbols taken in from and/or sent out to the environment as strings, we get a model for computations on strings, which can even be interpreted as representations of elements of a group based on a computable finite presentation.
We continue the investigations concerning the possibility of using spiking neural P systems as a ... more We continue the investigations concerning the possibility of using spiking neural P systems as a framework for solving computationally hard problems, addressing two problems which were already recently considered in this respect: Subset Sum and SAT: For both of them we provide uniform constructions of standard spiking neural P systems (i.e., not using extended rules or parallel use of rules) which solve these problems in a constant Keywords Membrane computing Á Spiking neural P system Á SAT problem Á Subset sum problem Á Complexity 1 Introduction Spiking neural P systems (in short, SN P systems) were introduced in Ionescu et al. (2006) as a class of P systems which incorporate into membrane computing specific ideas from the way biological neurons communicate through electrical impulses of identical form (spikes). We refer to Ionescu et al. (2006) and to other papers which can be found at the Web site of membrane computing (The P Systems Web Page: http://psystems.disco. unimib.it.) for motivation and basic definitions. In short, an SN P system consists of a set of neurons placed in the nodes of a directed graph and sending signals (spikes, denoted in what follows by the symbol a) along the arcs of the graph (called synapses). The spikes evolve by means of rules which, in the first papers reported in this area, were of two types: (i) standard spiking rules, which are of the form E/a c ? a; d, where E is a regular expression over {a} and c, d are natural numbers such that c C 1, d C 0, and (ii) forgetting rules, of the form a s ? k, where s C 1 is a natural number. Using a rule of the former type means that if a neuron contains k spikes, k C c, and a k [ L(E), then it can consume c spikes and produce one spike, after a delay of d steps. This spike is sent to all neurons connected by an outgoing synapse from the neuron where the rule was applied. Using a forgetting rule means that s spikes are removed, provided that the neuron contains exactly s spikes. If two spiking rules can be used at the same time in a neuron (i.e., both their regular expressions describe the contents of that neuron), then one of them is non-deterministically chosen, but, by definition, in Ionescu et al. (2006) it is forbidden to have a spiking rule E/a c ? a; d and a forgetting rule a s ? k such that a s [ L(E). A common generalization of these types of rules was introduced in Chen et al. (2006b) and Pȃun and Pȃun (2007) under the name of extended rules. These rules are of the form E/a c ? a p ; d, with the meaning that when using the rule, c spikes are consumed and p spikes are produced. Because p can be 0 or greater than 0, we obtain a generalization of both standard spiking and forgetting rules, with the additional feature of having the forgetting rules controlled by regular expressions. Moreover, forgetting rules are now allowed to compete in a non-deterministic way with firing rules. In each time unit (a common clock is assumed to exist, marking the time for all neurons), each neuron which can use a rule, of any type, has to do it (each neuron can use at most one rule, but the neurons work synchronously, evolving in parallel). One of the neurons is considered to be the output neuron, and its spikes are also sent to the environment. The moments of time when (at least) a spike is emitted by the output neuron are marked with 1, the other moments are marked with 0. This binary sequence is called the spike train produced by the system-it is infinite if the computation does not halt. With a spike train we can associate various numbers, which can be considered as computed (we also say generated) by an SN P system. For instance, in Ionescu et al. (2006) only the distance between the first two spikes of a spike train was considered, while in Pȃun et al. (2002) several extensions were examined which we do not mention here. An SN P system can also work in the accepting mode: a neuron is designated as the input neuron and a spike train is introduced in it; this spike train is accepted if the computation halts. In particular, we can introduce a spike train with only two spikes, coming at an interval of n steps, and then we say that the number n is accepted if the computation halts.
Annals of West University of Timisoara - Mathematics and Computer Science, 2019
The previous title takes some precautions, which are visible, but still I want to stress them. Fi... more The previous title takes some precautions, which are visible, but still I want to stress them. First, the autobiographical character. The last two decades-to be precise, the last twenty two years-I was totally dedicated to bio-computability, one can even say that I was confiscated by this research area, so fascinating, promising, endless in possibilities of theoretical developments and of applications. The beginning is placed in the spring of 1994, when I read a paper by Tom Head, a wise American who later became a friend and a collaborator of mine, who, already in 1987, proposed a formal language theory model for the recombination operation of DNA under the influence of restriction enzymes and ligase. He has named it the splicing operation. I will shortly describe it later. I remember it exactly-I was in Austria, in Graz, participating in a conference. On the one hand, I became immediately enthusiastic about this idea-after two decades of research in formal language theory, I was subconsciously looking for areas to apply this theory, on the other hand, I was somewhat unsatisfied, because Head's formalization was complex, it remained, to my taste, too close to the biological reality. Right then, in the hotel in Graz, I have imagined a simpler definition, closer to the style I was used, I can call it Salomaa-Marcus style. Four years after that I have worked This is the English version of a lecture delivered on
A series of open problems and research topics are formulated, about numerical and spiking neural ... more A series of open problems and research topics are formulated, about numerical and spiking neural P systems, initially prepared as a working material for a three months research stage of the second and the third co-author in Curtea de Argeş, Romania, in the fall of 2015. Further problems were added during this period, while certain problems were addressed in this time; some details and references are provided for such cases.
As mentioned above, the meeting was organized by the Research Group on Natural Computing from Sev... more As mentioned above, the meeting was organized by the Research Group on Natural Computing from Sevilla University (http://www.gcn.us.es) and all its members were enthusiastically involved in this (not always easy) work.
Spiking neural P systems (SN P systems, for short) are much investigated in the last years in mem... more Spiking neural P systems (SN P systems, for short) are much investigated in the last years in membrane computing, but still many open problems and research topics are open in this area. Here, we first recall two such problems (both related to neural biology) from [15]. One of them asks to build an SN P system able to store a number, and to provide it to a reader without losing it, so that the number is available for a further reading. We build here such a memory module and we discuss its extension to model/implement more general operations, specific to (simple) data bases. Then, we formulate another research issue, concerning pattern recognition in terms of SN P systems. In the context, we define a recent version of SN P systems, enlarged with rules able to request spikes from the environment; based on this version, so-called SN dP systems were recently introduced, extending to neural P systems the idea of a distributed dP automaton. Some details about such devices are also given, as a further invitation to the reader to this area of research.
A series of open problems and research topics are formulated, about numerical and spiking neural ... more A series of open problems and research topics are formulated, about numerical and spiking neural P systems, initially prepared as a working material for a three months research stage of the second and the third co-author in Curtea de Argeş, Romania, in the fall of 2015. Further problems were added during this period, while certain problems were addressed in this time; some details and references are provided for such cases.
In the style of previous meetings in this series, the ninth BWMC was conceived as a period of act... more In the style of previous meetings in this series, the ninth BWMC was conceived as a period of active interaction among the participants, with the emphasis on exchanging ideas and on cooperation. Interesting enough, both the number of presentations and the number of participants have continuously increased in the last years. (The list of the participants is given in the end of this preface.) However, in the style of the of this series of meeting, these presentations were \provocative", mainly proposing new ideas, open problems, research topics, results which need further improvements. The eciency of this type of meetings was again proved to be very high and the present volume proves this assertion. The papers included in this volume, arranged in the alphabetic order of the authors, were collected in the form available at a short time after the brainstorming; several of them are still under elaboration. The idea is that the proceedings are a working instrument, part of the interaction started during the stay of authors in Sevilla, meant to make possible a further cooperation, this time having a written support. A selection of the papers from this volume will be considered for publication in a special issues of
Two research directions on numerical P systems and two on spiking neural P systems which were rec... more Two research directions on numerical P systems and two on spiking neural P systems which were recently explored are shortly discussed. They deal with very natural versions of these classes of P systems which were not investigated before. Besides definitions, one recalls a few of the results obtained about these new classes of P systems and one points out open problems and directions for further research.
As mentioned above, the meeting was organized by the Research Group on Natural Computing from Sev... more As mentioned above, the meeting was organized by the Research Group on Natural Computing from Sevilla University (http://www.gcn.us.es)-and all the members of this group were enthusiastically involved in this (not always easy)
We continue the line of research of deterministic parallel non-cooperative multiset rewriting wit... more We continue the line of research of deterministic parallel non-cooperative multiset rewriting with control. We here generalize control, i.e., rule applicability context conditions, from promoters and inhibitors checking presence or absence of certain object up to some bound, to regular and even stronger predicates, focusing at predicates over multiplicity of one symbol at a time. 3 the meaning of a promoter-set in [3] is different, but the computational power results are equivalent up to the descriptional complexity parameters such as number of promoters/inhibitors and their weights
This note considers three basic research directions in membrane computing-characterizations of th... more This note considers three basic research directions in membrane computing-characterizations of the computing power of Turing machines, computing more than Turing machines, efficiency (solving computationally hard problems in a feasible time)-by basic classes of P systems (cell and tissue multiset rewriting systems, symport/antiport systems, spiking neural P systems, numerical P systems). (Types of) Results reported in the literature are briefly mentioned, several unsolved cases are pointed out, and directions of further research are proposed.
International Journal of Computers Communications & Control, 2015
Three are the points we briefly discuss here: using membrane computing tools for efficient comput... more Three are the points we briefly discuss here: using membrane computing tools for efficient computing/optimization, the possibilities of using “general" membrane computing (P systems using multisets of symbol objects processed by biochemical-like evolution rules) as a framework for modeling economic processes, and the numerical P systems, a class of computing devices explicitly defined with a motivation related to economics. The discussion is rather informal, only pointing out research directions and providing bibliographical information.
Seventh Brainstorming Week on Membrane Computing Vol 2 Miguel Angel Martinez Del Amor 2009 Isbn 9788461328390 Pags 197 206, 2009
A few open problems and research topics collected during the 7th Brainstorming Week on Membrane C... more A few open problems and research topics collected during the 7th Brainstorming Week on Membrane Computing are briefly presented; further details can be found in the papers included in the volume.
In search for "realistic" bio-inspired computing models, we consider asynchronous spiking neural ... more In search for "realistic" bio-inspired computing models, we consider asynchronous spiking neural P systems, in the hope to get a class of computing devices with decidable properties. However, although the non-synchronization is known in general to decrease the computing power, in the case of using extended rules (several spikes can be produced by a rule) we obtain again the equivalence with Turing machines (interpreted as generators of sets of vectors of numbers). The problem remains open for the case of restricted spiking neural P systems, whose rules can only produce one spike. On the other hand, we prove that asynchronous spiking neural P systems, with a specific way of halting, using extended rules and where each neuron is either bounded or unbounded, are equivalent to partially blind counter machines and, therefore, have many decidable properties.
In order to enhance the efficiency of spiking neural P systems, we introduce the features of neur... more In order to enhance the efficiency of spiking neural P systems, we introduce the features of neuron division and neuron budding, which are processes inspired by neural stem cell division. As expected (as it is the case for P systems with active membranes), in this way we get the possibility to solve computationally hard problems in polynomial time. We illustrate this possibility with SAT problem.
The concept of a matter object being annihilated when meeting its corresponding anti-matter objec... more The concept of a matter object being annihilated when meeting its corresponding anti-matter object is investigated in the context of membrane systems, i.e., of (distributed) multiset rewriting systems applying rules in the maximally parallel way. Computational completeness can be obtained with using only non-cooperative rules besides these matter/anti-matter annihilation rules if these annihilation rules have priority over the other rules. Without this priority condition, in addition catalytic rules with one single catalyst are needed to get computational completeness. Even deterministic systems are obtained in the accepting case. Universal P systems with a rather small number of rules-57 for computing systems, 59 for generating and 52 for accepting systemscan be constructed when using non-cooperative rules together with matter/anti-matter annihilation rules having weak priority. Allowing anti-matter objects as input and/or output, we even get a computationally complete computing model for computations on integer numbers. Interpreting sequences of symbols taken in from and/or sent out to the environment as strings, we get a model for computations on strings, which can even be interpreted as representations of elements of a group based on a computable finite presentation.
We continue the investigations concerning the possibility of using spiking neural P systems as a ... more We continue the investigations concerning the possibility of using spiking neural P systems as a framework for solving computationally hard problems, addressing two problems which were already recently considered in this respect: Subset Sum and SAT: For both of them we provide uniform constructions of standard spiking neural P systems (i.e., not using extended rules or parallel use of rules) which solve these problems in a constant Keywords Membrane computing Á Spiking neural P system Á SAT problem Á Subset sum problem Á Complexity 1 Introduction Spiking neural P systems (in short, SN P systems) were introduced in Ionescu et al. (2006) as a class of P systems which incorporate into membrane computing specific ideas from the way biological neurons communicate through electrical impulses of identical form (spikes). We refer to Ionescu et al. (2006) and to other papers which can be found at the Web site of membrane computing (The P Systems Web Page: http://psystems.disco. unimib.it.) for motivation and basic definitions. In short, an SN P system consists of a set of neurons placed in the nodes of a directed graph and sending signals (spikes, denoted in what follows by the symbol a) along the arcs of the graph (called synapses). The spikes evolve by means of rules which, in the first papers reported in this area, were of two types: (i) standard spiking rules, which are of the form E/a c ? a; d, where E is a regular expression over {a} and c, d are natural numbers such that c C 1, d C 0, and (ii) forgetting rules, of the form a s ? k, where s C 1 is a natural number. Using a rule of the former type means that if a neuron contains k spikes, k C c, and a k [ L(E), then it can consume c spikes and produce one spike, after a delay of d steps. This spike is sent to all neurons connected by an outgoing synapse from the neuron where the rule was applied. Using a forgetting rule means that s spikes are removed, provided that the neuron contains exactly s spikes. If two spiking rules can be used at the same time in a neuron (i.e., both their regular expressions describe the contents of that neuron), then one of them is non-deterministically chosen, but, by definition, in Ionescu et al. (2006) it is forbidden to have a spiking rule E/a c ? a; d and a forgetting rule a s ? k such that a s [ L(E). A common generalization of these types of rules was introduced in Chen et al. (2006b) and Pȃun and Pȃun (2007) under the name of extended rules. These rules are of the form E/a c ? a p ; d, with the meaning that when using the rule, c spikes are consumed and p spikes are produced. Because p can be 0 or greater than 0, we obtain a generalization of both standard spiking and forgetting rules, with the additional feature of having the forgetting rules controlled by regular expressions. Moreover, forgetting rules are now allowed to compete in a non-deterministic way with firing rules. In each time unit (a common clock is assumed to exist, marking the time for all neurons), each neuron which can use a rule, of any type, has to do it (each neuron can use at most one rule, but the neurons work synchronously, evolving in parallel). One of the neurons is considered to be the output neuron, and its spikes are also sent to the environment. The moments of time when (at least) a spike is emitted by the output neuron are marked with 1, the other moments are marked with 0. This binary sequence is called the spike train produced by the system-it is infinite if the computation does not halt. With a spike train we can associate various numbers, which can be considered as computed (we also say generated) by an SN P system. For instance, in Ionescu et al. (2006) only the distance between the first two spikes of a spike train was considered, while in Pȃun et al. (2002) several extensions were examined which we do not mention here. An SN P system can also work in the accepting mode: a neuron is designated as the input neuron and a spike train is introduced in it; this spike train is accepted if the computation halts. In particular, we can introduce a spike train with only two spikes, coming at an interval of n steps, and then we say that the number n is accepted if the computation halts.
Uploads
Papers by George Paun